Question: Solve for $x$ and $y$ using elimination. ${6x+2y = 36}$ ${5x-2y = -3}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {6x+2y = 36}\thinspace$ to find $y$ ${6}{(3)}{ + 2y = 36}$ $18+2y = 36$ $18{-18} + 2y = 36{-18}$ $2y = 18$ $\dfrac{2y}{{2}} = \dfrac{18}{{2}}$ ${y = 9}$ You can also plug ${x = 3}$ into $\thinspace {5x-2y = -3}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - 2y = -3}$ ${y = 9}$